In this paper, we introduce LLMBridge, a new LLM based system for the task of end-to-end referential bridging resolution in English. Our bridging resolution pipeline combines heuristic pre/post-processing with the natural language inference ability that comes from LLMs. We evaluate our bridging resolution pipeline on 3 datasets which have been used for referential bridging resolution evaluation in English: ISNotes, BASHI, and GUMBridge. Comparison to previous bridging resolution systems shows that the performance of LLMBridge surpasses previous state-of-the-art (SoTA) systems for all 3 datasets in the challenging End-to-end Evaluation Setting, as well as the Basic Bridging Resolution Evaluation Setting (gold bridging anaphor given). We also conduct a thorough error analysis of the LLMBridge performance, examining what varieties of bridging remain difficult for LLM based systems to identify. With this paper, we release the code for the LLMBridge pipeline.